共查询到20条相似文献,搜索用时 0 毫秒
1.
WANG Zhi-Xiu ZHANG Xi-He SHEN Ke 《理论物理通讯》2008,50(7):215-219
The spatial structure of a Bose-Einstein condensate (BEC) loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control with linear feedback is presented in this paper. By using the method, we propose a scheme of controlling chaotic behavior in a BEC with atomic mirrors. The results of the computer simulation show that controlling the chaos into the stable states could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the system is negative. 相似文献
2.
The spatial structure of a Bose-Einstein Condensate (BEC) loaded into an optical lattice potential is investigated. We suggest
a method for generating chaos in BEC by modulating periodic signals to convert the regular states into chaotic states. The
maximal Lyapunov exponent is calculated as a function of modulation intensity and modulation frequency respectively, and the
chaotic orbits associated with the positive Lyapunov exponents.
相似文献
3.
The resistively-capacitively-inductively-shunted (RCL-shunted) Josephson junction (RCLSJJ) shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required. 相似文献
4.
The resistively--capacitively--inductively-shunted (RCL-shunted)
Josephson junction (RCLSJJ) shows chaotic behaviour under some
parameter conditions. Here a scheme for controlling chaos in the
RCLSJJ is presented based on the linear feedback theory. Numerical
simulations show that this scheme can be effectively used to control
chaotic states in this junction into stable periodic states.
Moreover, the different stable period states with different period
numbers can be obtained by appropriately adjusting the feedback
intensity and delay time without any pre-knowledge of this system
required. 相似文献
5.
We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrdinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated. 相似文献
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Control of chaos by a delayed continuous feedback is studied experimentally in a gas discharge plasma. The power spectrum, the maximum of Lyapunov exponents and the time series of the signals all indicate that the period-1 unstable periodic orbit is controlled successfully. The dependence of the control on the delay time and the feedback gain as well as the strength of white noise is also investigated in detail. The experimental results show that the scaling index of the control versus the strength of white noise is 1.995, which is very close to that obtained from the simple logistic map. 相似文献
8.
Kei Inoue 《Entropy (Basel, Switzerland)》2022,24(6)
The Lyapunov exponent is the most-well-known measure for quantifying chaos in a dynamical system. However, its computation for any time series without information regarding a dynamical system is challenging because the Jacobian matrix of the map generating the dynamical system is required. The entropic chaos degree measures the chaos of a dynamical system as an information quantity in the framework of Information Dynamics and can be directly computed for any time series even if the dynamical system is unknown. A recent study introduced the extended entropic chaos degree, which attained the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. Moreover, an improved calculation formula for the extended entropic chaos degree was recently proposed to obtain appropriate numerical computation results for multidimensional chaotic maps. This study shows that all Lyapunov exponents of a chaotic map can be estimated to calculate the extended entropic chaos degree and proposes a computational algorithm for the extended entropic chaos degree; furthermore, this computational algorithm was applied to one and two-dimensional chaotic maps. The results indicate that the extended entropic chaos degree may be a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics. 相似文献
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11.
Kei Inoue 《Entropy (Basel, Switzerland)》2021,23(11)
The Lyapunov exponent is primarily used to quantify the chaos of a dynamical system. However, it is difficult to compute the Lyapunov exponent of dynamical systems from a time series. The entropic chaos degree is a criterion for quantifying chaos in dynamical systems through information dynamics, which is directly computable for any time series. However, it requires higher values than the Lyapunov exponent for any chaotic map. Therefore, the improved entropic chaos degree for a one-dimensional chaotic map under typical chaotic conditions was introduced to reduce the difference between the Lyapunov exponent and the entropic chaos degree. Moreover, the improved entropic chaos degree was extended for a multidimensional chaotic map. Recently, the author has shown that the extended entropic chaos degree takes the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. However, the author has assumed a value of infinity for some numbers, especially the number of mapping points. Nevertheless, in actual numerical computations, these numbers are treated as finite. This study proposes an improved calculation formula of the extended entropic chaos degree to obtain appropriate numerical computation results for two-dimensional chaotic maps. 相似文献
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We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties. 相似文献
14.
M. A. Jafarizadeh S. Behnia S. Khorram H. Nagshara 《Journal of statistical physics》2001,104(5-6):1013-1028
We give hierarchy of one-parameter family (, x) of maps at the interval [0, 1] with an invariant measure. Using the measure, we calculate Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent of these maps analytically, where the results thus obtained have been approved with the numerical simulation. In contrary to the usual one-parameter family of maps such as logistic and tent maps, these maps do not possess period doubling or period-n-tupling cascade bifurcation to chaos, but they have single fixed point attractor for certain values of the parameter, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at those values of the parameter whose Lyapunov characteristic exponent begins to be positive. 相似文献
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研究了周期脉冲驱动下的玻色-爱因斯坦凝聚体系(BEC)的动力学演化.其中着重考虑了BEC原子间的非线性相互作用对量子棘齿效应的影响.数值计算结果表明,较弱的非线性相互作用可以减弱定向动量流的强度.而较强的非线性相互作用则会使量子棘齿效应消失甚至发生反转,即系统会出现反向的定向动量流,而且随着时间的演化,动量流会表现出微弱的饱和趋势.计算还发现,高阶量子共振下系统的棘齿效应变得很不明显,而且外部驱动势的周期噪声很容易破坏体系的棘齿效应.
关键词:
玻色-爱因斯坦凝聚
量子混沌
量子共振
棘齿效应 相似文献
17.
The dual-ring erbium-doped fibre laser shows a hyperchaotic behaviour under some conditions.The hyperchaotic behaviour can be well controlled to enter into periodicity by modulating the pumping in one of the two rings.The period is different for different modulation index at the same modulation frequency,or for different modulation frequency at the same modulation index. 相似文献
18.
In this paper the nonlinear dynamical behaviour of a quantum cellular neural network (QCNN)
by coupling Josephson circuits was investigated and it was shown that the
QCNN using only two of them can cause the onset of chaotic oscillation. The
theoretical analysis and simulation for the two Josephson-circuits-coupled
QCNN have been done by using the amplitude and phase as state variables. The
complex chaotic behaviours can be observed and then proved by calculating
Lyapunov exponents. The study provides valuable information about QCNNs for
future application in high-parallel signal processing and novel chaotic
generators. 相似文献
19.
Numerical analysis of weak optical positive feedback (OPF) controlling chaos is studied in a semiconductor laser.The physical model of controlling chaos produced via modulating the current of semiconductor laser is presented under the condition of OPF.We find the physical mechanism that the nonlinear gain coefficient and linewidth enhancement factor of the laser are affected by OPF so that the dynamical behaviour of the system can be efficiently controlled.Chaos is controlled into a single-periodic state,a dual-periodic state,a fri-periodic state,a quadr-periodic state,a pentaperiodic state,and the laser emitting powers are increased by OPF in simulations.Lastly,another chaos-control method with modulating the amplitude of the feedback light is presented and numerically simulated to control chaotic laser into multi-periodic states. 相似文献
20.
S Rajasekar 《Pramana》1997,48(1):249-258
In this paper we consider the Bonhoeffer-van der Pol (BVP) equation which describes propagation of nerve pulses in a neural
membrane, and characterize the chaotic attractor at various bifurcations, and the probability distribution associated with
weak and strong chaos. We illustrate control of chaos in the BVP equation by the Ott-Grebogi-Yorke method as well as through
a periodic instantaneous burst. 相似文献